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A general mathematical property obeyed by mathematical objects in which all elements are within a neighborhood of nearby points. The continuous maps between topological ...

The cycle double cover conjecture states that every bridgeless graph has a collection of cycles which together contain every edge exactly twice. This conjecture remains open, ...

kappa(d)={(2lneta(d))/(sqrt(d)) for d>0; (2pi)/(w(d)sqrt(|d|)) for d<0, (1) where eta(d) is the fundamental unit and w(d) is the number of substitutions which leave the ...

An object created by folding a piece of paper along certain lines to form loops. The number of states possible in an n-flexagon is a Catalan number. By manipulating the ...

A Lehner continued fraction is a generalized continued fraction of the form b_0+(e_1)/(b_1+(e_2)/(b_2+(e_3)/(b_3+...))) where (b_i,e_(i+1))=(1,1) or (2, -1) for x in [1,2) an ...

The second theorem of Mertens states that the asymptotic form of the harmonic series for the sum of reciprocal primes is given by sum_(p<=x)1/p=lnlnx+B_1+o(1), where p is a ...

Modus tollens is a valid argument form in propositional calculus in which p and q are propositions. If p implies q, and q is false, then p is false. Also known as an indirect ...

The orthogonal decomposition of a vector y in R^n is the sum of a vector in a subspace W of R^n and a vector in the orthogonal complement W^_|_ to W. The orthogonal ...

If the vertices A, B, and C of triangle DeltaABC lie on sides QR, RP, and PQ of the triangle DeltaPQR, then the three circumcircles CBP, ACQ, and BAR have a common point X. ...

It is possible to describe a set of positive integers that cannot be listed in a book containing a set of counting numbers on each consecutively numbered page. Another form ...